{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8d44a155",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:08:33.521436Z",
     "start_time": "2023-07-28T14:08:33.296330Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MultipleLocator\n",
    "\n",
    "LEARNING_RATE = 1e-3\n",
    "EPOCHS = 4\n",
    "STEPS_IN_EPOCH = 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8c8e570a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:08:34.470476Z",
     "start_time": "2023-07-28T14:08:34.466145Z"
    }
   },
   "outputs": [],
   "source": [
    "def lr_step_values(scheduler):\n",
    "    # Get learning rates as each training step\n",
    "    learning_rates = []\n",
    "    # EPOCHS*STEPS_IN_EPOCH：表示总的优化步（optimizer steps）\n",
    "    for i in range(EPOCHS*STEPS_IN_EPOCH):\n",
    "        optimizer.step()\n",
    "        learning_rates.append(optimizer.param_groups[0][\"lr\"])\n",
    "        scheduler.step()\n",
    "    return learning_rates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f9b87a2c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:08:35.480434Z",
     "start_time": "2023-07-28T14:08:35.472037Z"
    }
   },
   "outputs": [],
   "source": [
    "def vis_lr_values(lr_values, title=''):\n",
    "    # Visualize learinig rate scheduler\n",
    "    fig, ax = plt.subplots(1,1, figsize=(10,5))\n",
    "    ax.plot(range(EPOCHS*STEPS_IN_EPOCH), \n",
    "            lr_values,\n",
    "            marker='o', \n",
    "            color='black')\n",
    "    ax.set_xlim([0, EPOCHS*STEPS_IN_EPOCH])\n",
    "    ax.set_ylim([0, LEARNING_RATE + 0.0001])\n",
    "    ax.set_xlabel('Steps')\n",
    "    ax.set_ylabel('Learning Rate')\n",
    "    ax.set_title(title)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.xaxis.set_major_locator(MultipleLocator(STEPS_IN_EPOCH))\n",
    "    ax.xaxis.set_minor_locator(MultipleLocator(1))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "439d58a5",
   "metadata": {},
   "source": [
    "## StepLR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3545c7c9",
   "metadata": {},
   "source": [
    "$$\n",
    "\\eta_t = \\gamma \\eta_{t-1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7f10b659",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:17:46.585697Z",
     "start_time": "2023-07-26T14:17:46.567480Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import StepLR # Import your choice of scheduler here\n",
    "\n",
    "# Set model and optimizer\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = StepLR(optimizer, \n",
    "                   step_size = 4, # Period of learning rate decay\n",
    "                   gamma = 0.5) # Multiplicative factor of learning rate decay\n",
    "learning_rates_step = lr_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "833181ef",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:22:36.160937Z",
     "start_time": "2023-07-26T14:22:35.885318Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(learning_rates_step, 'StepLR')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fe87f3d",
   "metadata": {},
   "source": [
    "## ExponentialLR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87e11bb5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:21:41.710361Z",
     "start_time": "2023-07-26T14:21:41.702940Z"
    }
   },
   "source": [
    "$$\n",
    "\\begin{split}\n",
    "&\\eta_t = \\gamma \\eta_{t-1}\\\\\n",
    "&\\eta_t = \\gamma^{t-1}\\eta_1\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "- 与 StepLR 相比，没有稳定阶段（stage）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "062d7dfa",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:19:44.012525Z",
     "start_time": "2023-07-26T14:19:43.999923Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import ExponentialLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = ExponentialLR(optimizer, gamma=0.5)\n",
    "lr_values_exp = lr_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "086fa9de",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:22:44.764233Z",
     "start_time": "2023-07-26T14:22:44.504305Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(lr_values_exp, 'exp lr')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38bf9d8",
   "metadata": {},
   "source": [
    "## ConstantLR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a7b50ec",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:26:27.305951Z",
     "start_time": "2023-07-26T14:26:27.297863Z"
    }
   },
   "source": [
    "- factor 与 total_iters\n",
    "    - 在初始的 total_iters 内，lr = lr * factor\n",
    "    - 在 total_iters 之后，恢复到初始的 lr；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "0ff59550",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:24:26.964933Z",
     "start_time": "2023-07-26T14:24:26.955126Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import ConstantLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = ConstantLR(optimizer, factor=0.5, total_iters=8)\n",
    "lr_values_constant = lr_step_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4d8015db",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-26T14:24:53.197425Z",
     "start_time": "2023-07-26T14:24:52.949830Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(lr_values_constant, 'constant')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ed80a1d",
   "metadata": {},
   "source": [
    "## LinearLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ffa426eb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:33:33.565595Z",
     "start_time": "2023-07-28T14:33:33.554481Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import LinearLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = LinearLR(optimizer, start_factor=0.5, total_iters=4)\n",
    "lr_values_linear = lr_step_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "26291119",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:33:39.607246Z",
     "start_time": "2023-07-28T14:33:39.336857Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(lr_values_linear, 'linear')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13e53e8e",
   "metadata": {},
   "source": [
    "## Cosine LR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ea93278",
   "metadata": {},
   "source": [
    "- https://pytorch.org/docs/stable/generated/torch.optim.lr_scheduler.CosineAnnealingLR.html\n",
    "- CosineAnnealingLR vs. CosineAnnealingWarmRestarts\n",
    "    - CosineAnnealingLR：周期性的\n",
    "    - CosineAnnealingWarmRestarts：周期会不断变长\n",
    "        - 4->8->16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ce722e7a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:34:30.901702Z",
     "start_time": "2023-07-28T14:34:30.888242Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import CosineAnnealingLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = CosineAnnealingLR(optimizer, T_max=8, eta_min=1e-4)\n",
    "lr_values_cos = lr_step_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c1377989",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:34:32.695623Z",
     "start_time": "2023-07-28T14:34:32.421252Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(lr_values_cos, 'cos anneal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "84d7dd33",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:35:59.754068Z",
     "start_time": "2023-07-28T14:35:59.740326Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import CosineAnnealingWarmRestarts\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = CosineAnnealingWarmRestarts(optimizer, T_0=4, T_mult=2, eta_min=1e-4)\n",
    "lr_values_cos_warm = lr_step_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8c5b1ae9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:36:00.932900Z",
     "start_time": "2023-07-28T14:36:00.663491Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(lr_values_cos_warm, 'cos warm')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "593ddbad",
   "metadata": {},
   "source": [
    "## OneCycleLR, CyclicLR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a92b390",
   "metadata": {},
   "source": [
    "- OneCycleLR：全局的调度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6903e8ff",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:38:31.219589Z",
     "start_time": "2023-07-28T14:38:31.207431Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.optim.lr_scheduler import OneCycleLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = OneCycleLR(optimizer, \n",
    "                       max_lr=1e-3, \n",
    "                       epochs=4, steps_per_epoch=8, \n",
    "                       anneal_strategy='cos')\n",
    "lr_values_one_cycle = lr_step_values(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c5a54090",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:38:33.182305Z",
     "start_time": "2023-07-28T14:38:32.915486Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vis_lr_values(lr_values_one_cycle, 'one_cycle_cos')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4e391b9a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:38:36.744651Z",
     "start_time": "2023-07-28T14:38:36.148215Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.000000000062981e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from torch.optim.lr_scheduler import OneCycleLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = OneCycleLR(optimizer, \n",
    "                       max_lr=1e-3, \n",
    "                       epochs=4, steps_per_epoch=8, \n",
    "                       anneal_strategy='linear')\n",
    "lr_values_one_cycle = lr_step_values(scheduler)\n",
    "print(lr_values_one_cycle[-1])\n",
    "vis_lr_values(lr_values_one_cycle, 'one_cycle_linear')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b2287eac",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-07-28T14:21:46.918890Z",
     "start_time": "2023-07-28T14:21:46.659266Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0001\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from torch.optim.lr_scheduler import CyclicLR\n",
    "model = torch.nn.Linear(2, 1)\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=LEARNING_RATE)\n",
    "scheduler = CyclicLR(optimizer, base_lr=1e-4, max_lr=1e-3, \n",
    "                     step_size_up=4, step_size_down=8, \n",
    "                     mode='triangular')\n",
    "lr_values_cyclic = lr_step_values(scheduler)\n",
    "print(lr_values_cyclic[0])\n",
    "vis_lr_values(lr_values_cyclic, 'cyclic')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb2c7c1a",
   "metadata": {},
   "source": [
    "## ReduceLROnPlateauLR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8bdef18",
   "metadata": {},
   "source": [
    "- reduces the learning rate by when the metric has stopped improving. \n",
    "    - 自适应的，adaptive；"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "438cd249",
   "metadata": {},
   "source": [
    "## conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73eeb913",
   "metadata": {},
   "source": [
    "- https://towardsdatascience.com/a-visual-guide-to-learning-rate-schedulers-in-pytorch-24bbb262c863#b465"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c6f78967",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "182px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
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 "nbformat": 4,
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